Abstract : How can a robot estimate if a task can be carried on or not in a given environment ? Several works rely on affordances, borrowed from ecological psychology, to answer. In our view, to learn allowed actions requires to learn local and global dependence between sensors and effectors while the robot is active. To do so we identify the robot to a random sensorimotor network. In order to represent its activity we use probabilistic and statistical dependence measure. They make it possible to build matrices, graphs and simplicial complexes, then to study their spectral, topological and homological properties. Lastly the interest of these tools is assessed thanks to a simulated wheeled robot whose task is to achieve supervised and unsupervised classification of objects that allow pushability, or that don-t.